The travel time calculation of seismic wave propagation in synthetic earth models is a fundamental technique needed for Kirchhoff seismic modeling and migration. Migration is a process used to image the subsurface. In this paper, using layer-based models, a genetic algorithm (GA) approach is presented to calculate the travel time, and implement GA for Kirchhoff ray tracing modeling and Kirchhoff migration. We adopt 2D and 3D layer-based models to determine the suitability and correctness of the genetic algorithm for this application. The algorithmic approach used can be transformed into a hardware using fixed-point arithmetic. Examples of Kirchhoff modeling and migration show that our software algorithm works effectively, and the design simulation verifies the correctness of our travel time engine.